If you are looking for something involving slightly less maths to explain how the mach meter works the following might help. My use of the word “proportional” is not strictly mathematically correct in a few places, but this doesn’t negate the general argument.
Pdyn = 1/2Rho V squared
Where Pdyn is dynamic pressure, Rho is air density and V is TAS
Rearranging this gives
TAS = square root ( 2 x Pdyn / Rho)
So TAS is proportional to Pdyn / Rho ……Equation 1.
Increasing Static Pressure (Pstat) compresses the air, causing its density to increase.
Increasing temperature expands the air, causing its density to decrease.
So we can say that Rho is proportional to Pstat / temperature.
Rearranging this gives
Temperature is proportional to Pstat / Rho ……Equation 2.
LSS is proportional to the square root of temperature
So using equation …2 we can say that
LSS is proportional to Pstat / Rho ……Equation 3.
We now have the following
TAS is proportional to Pdyn / Rho ……Equation 1.
LSS is proportional to Pstat / Rho ……Equation 3.
We also know that Mach number = TAS /LSS....... Equation 4
Combining equations 1, 3 and 4 we can say that
Mach Number is proportional to (Pdyn / Rho) / (Pstat / Rho)
This simplifies to give
Mach Number is proportional to Pdyn / Pstat
The Mach meter takes in total pressure and static pressure and uses two capsules and a mechanical linkage to measure the ratio of Pdyn/Pstat.
The various equations provided in previous posts detail precisely how Mach Number and Pdyn/Pstat are related. The relationship is not a simple linear one so the figures that you have quoted in your initial post are not correct.
Last edited by keith williams; 11th Jul 2012 at 13:34.